When Jane Mayer published her 10,000-word article about Charles and David Koch in The New Yorker in August 2010, David Koch denounced her piece in print and, as she reports in her new book, “Dark Money: The Hidden History of the Billionaires Behind the Rise of the Radical Right,” a “private investigative firm with powerful political and law enforcement connections was retained.” While there was no hard evidence on who had hired the firm, “clues leading back to the Kochs were everywhere.”

That effort may have backfired: Since that first article, Ms. Mayer has followed the trail of the tax-deductible “dark money” the brothers have secretly donated to political causes; absorbed the work of dozens of outstanding independent investigative journalists; ferreted out articles, speeches and interviews the brothers, or their advisers, have given, many of them quite revelatory; and secured access to previously unpublished sources.

“Dark Money,” the result of Ms. Mayer’s research, is a persuasive, timely and necessary story of the Koch brothers’ empire. It may read overly long and include some familiar material, but only the most thoroughly documented, compendious account could do justice to the Kochs’ bizarre and Byzantine family history and the scale and scope of their influence.

Ms. Mayer begins with Fred Koch, the family patriarch. “Oddly enough,” she writes, “the fiercely libertarian Koch family owed part of its fortune to two of history’s most infamous dictators, Joseph Stalin and Adolf Hitler,” for whose regimes Mr. Koch’s company built oil refineries in the 1930s.

Largely because of his experience in the Soviet Union, Fred Koch became a staunch anti-Communist and, in 1958, one of the 11 founding members of the John Birch Society. His son Charles did not fully commit himself to his father’s political project until the mid-1970s, when, Ms. Mayer writes, Charles Koch “began planning a movement that could sweep the country.” His declared goal? Nothing less than destroying what he referred to as “the prevalent statist paradigm.”

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Jane MayerCreditStephen Voss

The 1980 platform of the Libertarian Party, to which the Koch brothers provided financial support and on which David Koch ran for vice president, offered a preview of their anti-government zealotry. The Libertarians opposed federal income and capital gains taxes. They called for the repeal of campaign finance laws; they favored the abolition of Medicaid and Medicare and advocated the abolition of Social Security and the elimination of the Federal Election Commission, the Securities and Exchange Commission, the Environmental Protection Agency, the Food and Drug Administration and the Occupational Safety and Health Administration. “The platform was, in short,” Ms. Mayer concludes, “an effort to repeal virtually every major political reform passed during the 20th century.”

Not surprisingly, given the extremism of their views, which William F. Buckley Jr. characterized as “Anarcho-Totalitarianism,” the Libertarians polled less than 1 percent of the votes. Ronald Reagan was elected president.

As Ms. Mayer notes, the Kochs, instead of accepting the voters’ verdict, chose to spend money changing the way Americans voted. “During the next three decades,” Ms. Mayer writes, “they contributed well over $100 million, much of it undisclosed, to dozens of seemingly independent organizations aimed at advancing their radical ideas.”

When the Supreme Court in the 2010 Citizens United case permitted nonprofits to spend money on political campaigning, the Koch brothers funded their own political machine, which, in size, dollars and sophistication, rivaled that of the two major parties. Their success in the 2010 midterm election was remarkable, and, Ms. Mayer says, took the Democrats by surprise. Republicans picked up seats in the House and the Senate and 675 in state legislatures. “As a consequence of their gains, Republicans now had four times as many districts to gerrymander as the Democrats” and the legislative power to pass a series of laws suppressing the vote of those who might not support their agenda.

The Kochs, Ms. Mayer is careful to remind us, are only one of several fabulously wealthy families that have tried to move America to the right. Their outsize influence is a result not only of their outsize fortune — according to Forbes magazine, the brothers are the fifth and sixth wealthiest Americans, with a combined family income larger than that of Bill Gates — but also of their intellectual prowess and organizational skills. For more than a decade, they have organized donor summits to which they have invited like-minded billionaires, political consultants, media celebrities and elected officials. At these meetings, plans are made, issues chosen, money raised, donations pooled, spending coordinated for the next election cycles.

The Koch brothers and their allies insist, and no doubt believe, that their war on big government has been motivated by their commitment to the individual freedoms that government interferes with. Still, “it was impossible not to notice,” Ms. Mayer writes, “that the political policies they embraced benefited their own bottom lines first and foremost. Lowering taxes and rolling back regulations, slashing the welfare state and obliterating the limits on campaign spending might or might not have helped others, but they most certainly strengthened the hand of extreme donors with extreme wealth.”

One of the more startling revelations in Ms. Mayer’s book concerns the number of billionaires in the Koch network who have had “serious past or ongoing legal problems” and whose companies have been fined for violations of the Clean Air and the Clean Water Acts. Koch Industries, she reports, has been perhaps the most flagrant and willful polluter and scofflaw. According to the Environmental Protection Agency’s database, it was the No. 1 producer of toxic waste in the country in 2012.

To protect their investments in coal and oil pipelines and refineries (somewhat pared down in the last decade), the Koch brothers have, Ms. Mayer points out, funded think tanks committed to raising doubt about climate change. They have also spent tens of millions of dollars to roll back environmental regulations and defund or abolish the federal agencies that write and enforce them.

There are signs that the Kochs’ influence may be waning. The Republican candidate they appeared to have favored, Gov. Scott Walker of Wisconsin, is no longer in the presidential race. Donald J. Trump, the candidate out in front, has made clear that he has no need for Koch money and has ridiculed those who “beg” for it. Still, as Ms. Mayer reports, twice as many Koch network dollars will be in play in 2016 than were in play in 2012: $889 million, only slightly less than the $1 billion that the Democratic and Republican national committees each expect to spend on the election.

David Nasaw is the Arthur M. Schlesinger Jr. Professor of History at the CUNY Graduate Center. His most recent book is “The Patriarch: the Remarkable Life and Turbulent Times of Joseph P. Kennedy.”

Dark Money

The Hidden History of the Billionaires Behind the Rise of the Radical Right

By Jane Mayer

449 pages. Doubleday. $29.95.

A version of this article appears in print on , on Page C1 of the New York edition with the headline: Powerful Brothers’ History Illuminated. Order Reprints | Today’s Paper | Subscribe